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This paper provides a survey of recent progress and software for
solving mixed integer nonlinear programs (MINLP) wherein the objective
and constraints are defined by convex functions and integrality
restrictions are imposed on a subset of the decision variables.
Convex MINLPs have received sustained attention in very years. By
exploiting analogies to the case of well-known techniques for solving
mixed integer linear programs and incorporating these techniques into
the software, significant improvements have been made in our ability
to solve the problems.